MinT - Best Known (180, 180+68, s)-Nets in Base 2

Best Known (180, 180+68, s)-Nets in Base 2

(180, 180+68, 195)-Net over F₂ — Constructive and digital

Digital (180, 248, 195)-net over F₂, using

1 times m-reduction [i] based on digital (180, 249, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 83, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(180, 180+68, 266)-Net over F₂ — Digital

Digital (180, 248, 266)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+68, 2074)-Net in Base 2 — Upper bound on s

There is no (180, 248, 2075)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 456 815788 069724 527824 918184 278932 368072 948450 868599 411710 644286 506142 748224 > 2²⁴⁸ [i]